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Small-x evolution in QCD is conveniently described by Mueller's dipole modelwhich, however, does not include saturation effects in a way consistent withboost invariance. In this paper we first show that the recently studied zeroand one dimensional toy models exhibiting saturation and explicit boostinvariance can be interpreted in terms positive definite k-> k+1 dipolevertices. Such k-> k+1 vertices can in the full model be generated by combiningthe usual dipole splitting with k-1 simultaneous dipole swings. We show that,for a system consisting of N dipoles, one needs to combine the dipole splittingwith at most N-1 simultaneous swings in order to generate all colourcorrelations induced by the multiple dipole interactions.

On the Dipole Swing and the Search for Frame Independence in the Dipole Model